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# Arithmetic Series

Sequence of Numbers in which difference between any two consecutive numbers is constant is known as arithmetic series. Arithmetic progression is denoted as i, i + d, i + 2d, i + 3d, i + 4d …...... i + (n – 1) d, here 'i' denotes initial value and 'd' denotes the common difference. For example: 20, 24, 28, 32, 36, 40 here initial value of A.P is 20 and difference between two numbers is 4. Now we will discuss how to find the sum of 'n' terms in series arithmetic.
Using formula we can calculate arithmetic series. Formula to calculate sum of 'n' terms in Arithmetic Progression is:
sum of n terms = n / 2 (2i + (n – 1) d).

Let’s understand this formula with help of an example:
Suppose we have to calculate sum of first 20 terms of arithmetic progression: 8, 3, -2..........and so on,
As we know that the sum of 'n' terms is given as:

sum of n terms = n / 2 (2i + (n – 1) d).
Here 'i' shows the initial value and value of a = 8, 'd' is common difference, value of d = 3 – 8 = -5, and value of 'n' = 20. So put these value in formula, we get:
sum of n terms = n / 2 (2i + (n – 1) d).
sum of n terms = 20 / 2 (2 * 8 + (20 – 1) (-5)),
sum of n terms = 10 (16 + (19) (-5)),
sum of n terms = 10 [16 – 95],
sum of n terms = 10 [-79],
sum of n terms = - 790,
So sum of first 20 terms is - 790. This is all about Arithmetic series.

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